Example2:
Computethe followingindefiniteintegral.
Solution:
Usingour ruleswe have
Sometimesour rulesneedto be modifiedslightlydue to operationswith constantsas is the casein the fol-
lowingexample.
Example3:
Computethe followingindefiniteintegral:
Solution:
We first note that our rule for integratingexponentialfunctionsdoesnot workhere since
However, if we rememberto dividethe originalfunctionby the constantthen we get the correctantiderivative
and have
We can now re-statethe rule in a moregeneralform as
DifferentialEquations
We concludethis lessonwith someobservationsaboutintegrationof functions.First,recallthat the integration
processallowsus to start with function from whichwe find anotherfunction such that